Asymmetric Gluon Distributions and Hard Diffractive Electroproduction

Due to the momentum transfer r ≡ p − p′ from the initial proton to the final, the “asymmetric” matrix element 〈p′|G . . . G|p〉 that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function fg(x). I outline a pQCD formalism based on a concept of a double distribution Fg(x, y), which specifies the fractions xp, yr, (1 − y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. I discuss the one-loop evolution equation for the double distribution Fg(x, y;μ) and obtain the solution of this equation in a simplified situation when the quark-gluon mixing effects are neglected. For r2 = 0, the momentum transfer r is proportional to p: r = ζp, and it is convenient to parameterize the matrix element 〈p − r|G . . . G|p〉 by an asymmetric distribution function F ζ (X) depending on the total fractions X ≡ x + yζ and X − ζ = x − (1 − y)ζ of the initial hadron momentum p carried by the gluons. I formulate evolution equations for F ζ (X), study some of their general properties and discuss the relationship between F ζ (X), Fg(x, y) and fg(x). Also Laboratory of Theoretical Physics, JINR, Dubna, Russian Federation